Reducing lens system

ABSTRACT

A reducing lens system consisting of three lens components, having an aperture ratio of F/8 with the capability of providing a good image over the entire image surface, and a vignetting factor of 100% capable of maintaining brightness of the image to the peripheral portions thereof.

BACKGROUND OF THE INVENTION

The present invention relates to a reducing lens system and more particularly to a lens system in which an original paper to be copied is projected with reduction in its size while keeping constant the distance between the surface of the original paper and the surface of the projection as well as the dimensions of the surface of the original paper and the surface of the projection.

Reducing lens systems of high speed having a relatively large aperture ratio have been known as being conventional, but there has not existed such a lens system that has the vignetting factor of 100% in order to keep the brightness of the image to its peripheral portions.

SUMMARY OF THE INVENTION

The object of the present invention is to provide a reducing lens system of low cost consisting three lens components, having an aperture ratio F:8 with the capability of providing a good image over the entire image surface, and a vignetting factor of 100% capable of maintaining brightness of the image to the peripheral portion thereof.

As shown in FIG. 1, a reducing lens system of the present invention is constituted of a first lens component of a positive lens, a second lens component of a negative lens and a third lens component of a positive lens, the lens system satisfying the following conditions.

    ______________________________________                                         (1)           1.73 > n.sub.3 ≧ n.sub.1 > 1.63                                         1.65 > n.sub.2 > 1.59                                            (2)           61 > ν.sub.1 , ν.sub.3 > 54                                              36 > ν.sub.2 > 33                                             (3)           0.76f > f.sub.1 > 0.71f                                                        -0.30f > f.sub.2 > -0.35f                                                      0.48f > f.sub.3 > 0.44f                                          (4)           0.14f > d.sub.1, d.sub.2, d.sub.5 > 0.11f                                      0.51f > Σd > 0.48f                                         (5)           0.52f > r.sub.1 > 0.49f                                                        -6.2f > r.sub.2 > -17.0f                                                       -0.43f > r.sub.3 > -0.48f                                                      0.38f > r.sub.4 > 0.32f                                                        1.32f > r.sub.5 > 1.12f                                                        -0.39f > r.sub.6 > -0.44f                                        ______________________________________                                    

wherein the reference symbols n₁, n₂ and n₃ represent the refractive indices of the respective lenses, the symbols ν₁, ν₂ and ν₃ represent the Abbe numbers of the respective lenses, the symbol f represents the focal length of the total lens system, the symbol d₁ and d₅ represent the axial thicknesses of the first and third lens components, the symbol d₂ represents the axial air space between the first and the second lens components, the symbol ρd represents the total length of the lens system and the symbol r₁ through r₆ represent the radii of curvature of the respective lens surfaces, respectively.

The object of the present invention is to provide a reducing lens system which has the reduction ratio of 1/10 and the vignetting factor of 100%. For this purpose, it is necessary both to decrease the coma flare and to obtain a good symmetry of coma. Therefore, the incident height of the ray of light entering the second and third lens components and the symmetry of the expanded luminous fluxes must be appropriate. For this reason, the distribution of the respective lens powers should be as given in condition (3). Under such power distribution in the respective lenses, in order to decrease the Petzval sum, the expression ##EQU1## must be zero. In view of f₁, f₃ >0, f₂ <0, that is ##EQU2## the condition must be n₃ ≧n₁ >n₂. In order to correct the chromatic aberration in the lens system as according to the present invention, the Abbe numbers ν₁, ν₂ and ν₃ of the respective lenses must be ν₁, ν₃ >ν₂ and the larger the differences between ν₁ and ν₂ and between ν₃ and ν₂ the better the effectiveness. Conditions (1) and (2) have been established in order to improve the Petzval sum and the chromatic aberration with the above mentioned points taken into account.

Under condition (1), when n₁ exceeds the lower limit, the Petzval sum is under-corrected. When n₂ exceeds the upper limit, the Petzval sum is likewise under-corrected. When n₃ exceeds the upper limit and n₂ the lower limit, the Petzval sum is well-corrected. However, it then becomes difficult to obtain the glass material which satisfies the requirements that the Abbe numbers ν₁ and ν₃ of the first lens component and the third lens component must be large and the Abbe number ν₂ of the second lens component must be small in order to correct the chromatic aberration. Under condition (1), although the lower limits of n₁ and n₃ are slightly smaller than the upper limit of n₂, the relation must be n₃ ≧n₁ >n₂ and, therefore, it is necessary to meet this relation in selecting the glass material.

Next, under condition (2), when ν₁ and ν₃ exceed the lower limit, the axial chromatic aberration becomes large. When ν₁ and ν₃ exceed the upper limit, it becomes difficult to obtain a glass material which satisfies n₃ ≧n₁ >1.63 of condition (1) for the purpose of correcting the Petzval sum. When ν₂ exceeds the upper limit, the axial chromatic aberration becomes large and when ν₂ exceeds the lower limit, it becomes difficult to obtain a glass material which satisfies 1.65>n₂ of condition (1).

Under condition (3), when f₁ exceeds the lower limit, the Petzval sum is under-corrected and the coma flare increases. When f₁ exceeds the upper limit, the spherical aberration is under-corrected and the symmetry of the coma is deteriorated. When f₂ exceeds the upper limit, although this is good for correcting the Petzval sum, the spherical aberration becomes large in the positive direction and the coma flare is increased. When f₂ exceeds the lower limit, the Petzval sum is under-corrected and symmetry of the coma is deteriorated. When f₃ exceeds the upper limit, although this is good for correcting the Petzval sum, the symmetry of the coma and the astigmatism are deteriorated. When f₃ exceeds the lower limit, the Petzval sum becomes large and the coma flare is increased.

As shown in condition (4), d₁, d₂ and d₅ are long relative to the total length of the lens system and this is necessary to keep a good symmetry of the luminous flux, that is, the symmetry of the coma. When d₁, d₂ and d₅ exceed the upper limit of condition (4), the spherical aberration is over-corrected and the astigmatism becomes large in the negative direction so that the symmetry of the coma is improved but the coma flare increases over the entire image surface. When these values exceed the lower limit of condition (4), the symmetry of the coma is deteriorated and the axial chromatic aberration becomes large.

As according to condition (4), by increasing d₁ and d₅, that is, by increasing the axial thicknesses of the first lens component and the third lens component, the radii of curvature r₂ and r₅ of the surface at the image side of the first lens component and the surface of the object side of the third lens component can be increased thereby to improve the correction of spherical aberration. Under condition (5), when r₂ and r₅ exceed the lower limit, the spherical aberration is over-corrected and the coma flare increases. This is due to the fact that when r₂ exceeds the lower limit, the incident height of the ray entering the second lens component becomes large so that the influence on the spherical aberration by the negative lens is increased. At the same time, the incident of height of the ray entering the third lens component also becomes large so that, in order to obtained required reduction ratio, the compensation must be made by decreasing r₅, in which case the coma flare increases. And, when r₂ and r₅ exceed the upper limit, the distortion becomes large and the symmetry of the coma deteriorates.

As explained above, the surfaces r₂ and r₅ are effective surfaces for the correction of the spherical aberration but these surfaces also have great influences on the coma. As shown under condition (4), by appropriately selecting d₁ and d₅, etc., the influences on the coma and the symmetry concerning the above mentioned surfaces are moderated.

With reference to r₁ and r₆, when they exceed the upper limit of condition (5), the spherical aberration is over-corrected, and when they exceed the lower limit, the inclination of these surfaces with respect to the incident and exit luminous fluxes becomes large and the coma flare is increased. When r₃ and r₄ exceed the upper limit of condition (5), the coma flare is increased, and when they exceed the lower limit, the spherical aberration is increased in the positive direction.

Further objects and advantages will be apparent in the arrangement as set forth in the following specification taken together with the accompanying drawings.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a sectional view of a reducing lens system according to the present invention.

FIGS. 2 through 6 show graphs illustrating conditions of aberration of the embodiments 1 through 5.

DESCRIPTION OF THE PREFERRED EMBODIMENTS

Now, some preferred embodiments of the present invention relating to the reducing lens system as described above are given below:

    ______________________________________                                         Embodiment 1                                                                     f = 100   F/8                                                                r.sub.1 = 51.183                                                                 d.sub.1 = 12.92                                                                          n.sub.1 = 1.6968                                                                               ν.sub.1 = 56.49                                 r.sub.2 = -1630.462                                                              d.sub.2 = 13.505                                                             r.sub.3 = -45.819                                                                d.sub.3 = 2.205                                                                          n.sub.2 = 1.64769                                                                              ν.sub.2 = 33.8                                  r.sub.4 = 35.849                                                                 d.sub.4 = 9.569                                                              r.sub.5 = 130.152                                                                d.sub.5 = 12.712                                                                         n.sub.3 = 1.6968                                                                               ν.sub.3 = 56.49                                 r.sub.6 = -39.39                                                                 f.sub.1 = 71.444                                                                           f.sub.2 = -30.727                                                  f.sub.3 = 44.775                                                                          ##STR1##                                                          Embodiment 2                                                                     f = 100   F/8                                                                r.sub.1 = 49.132                                                                 d.sub.1 = 12.451                                                                         n.sub.1 = 1.6516                                                                               ν.sub.1 = 58.7                                  r.sub.2 = -1513.905                                                              d.sub.2 = 12.257                                                             r.sub.3 = -47.702                                                                d.sub.3 = 2.711                                                                          n.sub.2 = 1.64769                                                                              ν.sub.2 = 33.8                                  r.sub.4 = 37.053                                                                 d.sub.4 = 8.934                                                              r.sub.5 = 122.6                                                                  d.sub.5 = 12.946                                                                         n.sub.3 = 1.72916                                                                              ν.sub.3 = 54.7                                  r.sub.6 = -43.053                                                                f.sub.1 = 73.262                                                                           f.sub.2 = -31.798                                                  f.sub.3 = 45.188                                                                          ##STR2##                                                          Embodiment 3                                                                     f = 100   F/8                                                                r.sub.1 = 50.133                                                                 d.sub.1 = 12.169                                                                         n.sub.1 = 1.64  ν.sub.1 = 60.1                                  r.sub.2 = -896.534                                                               d.sub. 2 = 11.592                                                            r.sub.3 = -47.427                                                                d.sub.3 = 2.869                                                                          n.sub.2 = 1.5927                                                                               ν.sub.2 = 35.3                                  r.sub.4 = 35.929                                                                 d.sub.4 = 9.019                                                              r.sub.5 = 114.024                                                                d.sub.5 = 13.164                                                                         n.sub.3 = 1.67  ν.sub.3 = 57.3                                  r.sub.6 = -42.142                                                                f.sub.1 = 74.559                                                                           f.sub.2 = -34.054                                                f.sub.3 = 47.533                                                                            ##STR3##                                                          Embodiment 4                                                                     f = 100   F/8                                                                r.sub.1 = 49.764                                                                 d.sub.1 = 12.513                                                                         n.sub.1 = 1.63854                                                                              ν.sub.1 = 55.4                                  r.sub.2 = -636.878                                                               d.sub.2 = 12.518                                                             r.sub.3 = -43.733                                                                d.sub.3 = 2.614                                                                          n.sub.2 = 1.5927                                                                               ν.sub.2 = 35.3                                  r.sub.4 = 33.216                                                                 d.sub.4 = 9.367                                                              r.sub.5 = 113.146                                                                d.sub.5 = 12.91                                                                          n.sub.3 = 1.6583                                                                               ν.sub.3 = 57.3                                  r.sub.6 = -38.61                                                                 f.sub.1 = 72.803                                                                           f.sub.2 = -31.453                                                  f.sub.3 = 45.257                                                                          ##STR4##                                                          Embodiment 5                                                                     f = 100   F/8                                                                r.sub.1 = 50.993                                                                 d.sub.1 = 12.266                                                                         n.sub.1 = 1.6516                                                                               ν.sub.1 = 58.7                                  r.sub.2 = -1149.926                                                              d.sub.2 = 11.864                                                             r.sub.3 = -47.83                                                                 d.sub.3 = 2.727                                                                          n.sub.2 = 1.5927                                                                               ν.sub.2 = 35.3                                  r.sub.4 = 36.349                                                                 d.sub.4 = 9.171                                                              r.sub.5 = 118.648                                                                d.sub. 5 = 13.111                                                                        n.sub.3 = 1.6779                                                                               ν.sub.3 = 55.3                                  r.sub.6 = -42.559                                                                f.sub.1 = 75.238                                                                f.sub.3 = 47.776.2 = -                                                                   ##STR5##                                                          ______________________________________                                    

wherein the reference symbols r₁ through r₆ represent the radii of curvature of the respective lenses surfaces, the symbols d₁ through d₅ represent the axial thicknesses and the axial air space of the respective lenses, the symbols n₁ through n₃ represent the refractive indices of the respective lenses and the symbols ν₁ through ν₃ represent the Abbe numbers of the respective lenses, respectively.

Seidel's coefficients of these embodiments are given below:

    ______________________________________                                         Spherical                             Petzval                                  aberration                                                                               Astigmatism                                                                               Coma     Distortion                                                                             sum                                      ______________________________________                                         Embodiment 1                                                                   1   2.6014    0.0193     0.2243 0.0781  0.8869                                 2   1.6555    2.0302     -1.8333                                                                               -2.2791 0.0278                                 3   -8.4156   -2.7659    4.8246 2.1294  -0.9483                                4   -8.8475   -1.1458    -3.1839                                                                               -0.8485 -1.2120                                5   2.1868    1.3571     1.7227 1.3438  0.3488                                 6   11.3327   0.3751     -2.0619                                                                               -0.2779 1.1524                                 Σ                                                                            0.5132    -0.13      -0.3075                                                                               0.1458  0.2555                                 Embodiment 2                                                                   1   2.9078    0.0295     0.2928 0.0923  0.8872                                 2   1.5243    1.7869     -1.9659                                                                               -1.9659 0.0288                                 3   -8.3489   -2.5715    1.9324 1.9324  -0.9104                                4   -9.5260   -1.1746    -0.8240                                                                               -0.8240 -1.1721                                5   2.6241    1.3876     1.2854 1.2854  0.3800                                 6   10.4065   0.4301     -0.3075                                                                               -0.3075 1.0821                                 Σ                                                                            -0.4121   -0.1119    0.2128 0.2128  0.2956                                 Embodiment 3                                                                   1   2.7473    0.0437     0.3465 0.1139  0.8592                                 2   1.5601    1.7179     -1.6371                                                                               -1.8532 0.0480                                 3   -8.3565   -2.4333    4.5093 1.7804  -0.8660                                4   -9.3285   -1.0904    -3.1893                                                                               -0.7636 -1.1432                                5   2.3761    1.2624     1.7319 1.2032  0.3883                                 6   10.6990   0.3915     -2.0466                                                                               -0.2759 1.0508                                 Σ                                                                            -0.3026   -0.1082    -0.2853                                                                               0.2048  0.3371                                 Embodiment 4                                                                   1   2.7742    0.0274     0.2757 0.0886  0.8642                                 2   1.7722    1.9093     -1.8395                                                                               -2.0519 0.0675                                 3   -9.1180   -2.6389    4.9053 1.9248  -0.9390                                4   -11.1155  -1.1464    -3.5698                                                                               -0.7652 -1.2364                                5   2.7797    1.3867     1.9633 1.2530  0.3872                                 6   12.5201   0.3431     -2.0725                                                                               -0.2446 1.1346                                 Σ                                                                            -0.3874   -0.1188    -0.3375                                                                               0.2046  0.2781                                 Embodiment 5                                                                   1   2.6272    0.0438     0.3391 0.1159  0.8540                                 2   1.4659    1.6974     -1.5774                                                                               -1.8672 0.0379                                 3   -8.0610   -2.4071    4.4050 1.7847  -0.8588                                4   -8.8828   -1.0730    -3.0873                                                                               -0.7657 -1.1301                                5   2.2021    1.2405     1.6528 1.2132  0.3759                                 6   10.4595   0.3964     -2.0362                                                                               -0.2812 1.0479                                 Σ                                                                            -0.1891   -0.1021    -0.3041                                                                               0.1996  0.3267                                 ______________________________________                                    

As explained hereinabove, the reducing lens system according to the present invention has a vignetting factor of 100% and provides the effect that a ray of light is not eclipsed and, thus, the brightness of the image is uniform to the periphery of image surface. The aperture ratio is F/8 and so the lens speed is high enough from the practical point of view. The lens system of this kind is sometimes used with parallel plain boards being placed on the surface of the original paper to be copied and on the surface of projection. However, with the lens system according to the present invention, whether the parallel plain boards are placed or removed, the aberrations are very little deteriorated and excellent image formation characteristics can be maintained. 

I claim:
 1. A reducing lens system comprising a first lens component of a biconvex lens, a second lens component of a biconcave lens and a third lens component of a biconvex lens, the said lens system satisfying the following conditions:

    ______________________________________                                         (1)           1.73 > n.sub.3 ≧ n.sub.1 > 1.63                                         1.65 > n.sub.2 > 1.59                                            (2)           61 > ν.sub.1 , ν.sub.3 > 54                                              36 > ν.sub.2 > 33                                             (3)           0.76f > f.sub.1 > 0.71f                                                        -0.30f > f.sub.2 > -0.35f                                                      0.48f > f.sub.3 > 0.44f                                          (4)           0.14f > d.sub.1, d.sub.2, d.sub.5 > 0.11f                                      0.51f > Σd > 0.48f                                         (5)           0.52f > r.sub.1 > 0.49f                                                        -6.2f > r.sub.2 > -17.0f                                                       -0.43f > r.sub.3 > -0.48f                                                      0.38f > r.sub.4 > 0.32f                                                        1.32f > r.sub.5 > 1.12f                                                        -0.39f > r.sub.6 > -0.44f                                        ______________________________________                                    

wherein the reference symbols n₁ through n₃ represent the refractive indices of the respective lenses, the symbols ν₁ through ν₃ represent the Abbe numbers of the respective lenses, the symbols f₁ through f₃ represent the focal length of the respective lenses, the symbols d₁ and d₅ represent the axial thicknesses of the first and third lens components, the symbol d₂ represents the axial air space between the first and second lens components, the symbol Σd represents the total length of the lens system, the symbols r₁ through r₆ represent the radii of curvature of the respective lens surfaces and the symbol f represents the focal length of the total lens system, respectively.
 2. A reducing lens system according to claim 1, having the following data:

    ______________________________________                                         f = 100   F/8                                                                  ______________________________________                                         r.sub.1 = 51.183                                                                         d.sub.1 = 12.92                                                                           n.sub.1 = 1.6968                                                                            ν.sub.1 = 56.49                           r.sub.2 = -1630.462                                                                      d.sub. 2 = 13.505                                                    r.sub.3 = 45.819                                                                         d.sub.3 = 2.205                                                                           n.sub.2 = 1.64769                                                                           ν.sub.2 = 33.8                            r.sub.4 = 35.849                                                                         d.sub.4 = 9.569                                                      r.sub.5 = 130.152                                                                        d.sub.5 = 12.712                                                                          n.sub.3 = 1.6968                                                                            ν.sub.3 = 56.49                           r.sub.6 = -39.39                                                                         f.sub.1 = 71.444                                                                          f.sub.2 = -30.717                                                   f.sub.3 = 44.775                                                                           ##STR6##                                                 ______________________________________                                    

wherein the reference symbols r₁ through r₆ represent the radii of curvature of the respective lens surfaces, the symbols d₁ through d₅ represent the axial thicknesses and the axial air spaces of the respective lenses, the symbols n₁ through n₃ represent the refractive indices of the respective lenses, the symbols ν₁ through ν₃ represent the Abbe numbers of the respective lenses and the symbol F represents the aperture ratio, respectively.
 3. A reducing lens system according to claim 1, having the following data:

    ______________________________________                                         f = 100   F/8                                                                  ______________________________________                                         r.sub.1 = 49.132                                                                         d.sub.1 = 12.451                                                                          n.sub.1 = 1.6516                                                                            ν.sub.1 = 58.7                            r.sub.2 = 1513.905                                                                       d.sub.2 = 12.257                                                     r.sub.3 = 47.702                                                                         d.sub.3 = 2.711                                                                           n.sub.2 = 1.64769                                                                           ν.sub.2 = 33.8                            r.sub.4 = 37.053                                                                         d.sub.4 = 8.934                                                      r.sub.5 = 122.6                                                                          d.sub.5 = 12.946                                                                          n.sub.3 = 1.72916                                                                           ν.sub.3 = 54.7                            r.sub.6 = -43.053                                                                        f.sub.1 = 73.262                                                                          f.sub.2 = -31.798                                                   f.sub.3 = 45.188                                                                           ##STR7##                                                 ______________________________________                                    

wherein the reference symbols r₁ through r₆ represent the radii of curvature of the respective lens surfaces, the symbols d₁ through d₅ represent the axial thicknesses and the axial air spaces of the respective lenses, the symbols n₁ through n₃ represent the refractive indices of the respective lenses, the symbols ν₁ through ν₃ represent the Abbe numbers of the respective lenses and the symbol F represents the aperture ratio, respectively.
 4. A reducing lens system according to claim 1, having the following data:

    ______________________________________                                          f = 100     F/8                                                               ______________________________________                                         r.sub.1   = 50.133                                                                       d.sub.1 = 12.169                                                                          n.sub.1 = 1.64                                                                              ν.sub.1 = 60.1                            r.sub.2 = 896.534                                                                        d.sub.2 = 11.592                                                     r.sub.3 = -47.427                                                                        d.sub.3 = 2.869                                                                           n.sub.2 = 1.5927                                                                            ν.sub.2 = 35.3                            r.sub.4 = 35.929                                                                         d.sub.4 = 9.019                                                      r.sub.5 = 114.024                                                                        d.sub.5 = 13.164                                                                          n.sub.3 = 1.67                                                                              ν.sub.3 = 57.3                            r.sub.6 = 42.142                                                                         f.sub.1 = 74.559                                                                          f.sub.2 = -34.054                                                   f.sub.3 = 47.533                                                                           ##STR8##                                                 ______________________________________                                    

wherein the reference symbols r₁ through r₆ represent the radii of curvature of the respective lens surfaces, the symbols d₁ through d₅ represent the axial thicknesses and the axial air spaces of the respective lenses, the symbols n₁ through n₃ represent the refractive indices of the respective lenses, the symbols ν₁ through ν₃ represent the Abbe numbers of the respective lenses and the symbol F represents the aperture ratio, respectively.
 5. A reducing lens system according to claim 1, having the following data:

    ______________________________________                                         f = 100   F/8                                                                  ______________________________________                                         r.sub.1 = 49.764                                                                         d.sub.1 = 12.513                                                                          n.sub.1 = 1.63854                                                                           ν.sub.1 = 55.4                            r.sub.2 = -636.878                                                                       d.sub.2 = 12.518                                                     r.sub.3 = -43.733                                                                        d.sub.3 = 2.614                                                                           n.sub.2 = 1.5927                                                                            ν.sub.2 = 35.3                            r.sub.4 = 33.216                                                                         d.sub.4 = 9.367                                                      r.sub.5 = 113.146                                                                        d.sub.5 = 12.91                                                                           n.sub.3 = 1.6583                                                                            ν.sub.3 = 57.3                            r.sub.6 = -38.61                                                                         f.sub.1 = 72.803                                                                          f.sub.2 = -31.453                                                   f.sub.3 = 45.257                                                                           ##STR9##                                                 ______________________________________                                    

wherein the reference symbols r₁ through r₆ represent the radii of curvature of the respective lens surfaces, the symbols d₁ through d₅ represent the axial thicknesses and the axial air spaces of the respective lenses, the symbols n₁ through n₃ represent the refractive indices of the respective lenses, the symbols ν₁ through ν₃ represent the Abbe numbers of the respective lenses and the symbol F represents the aperture ratio, respectively.
 6. A reducing lens system according to claim 1, having the following data:

    ______________________________________                                         f = 100   F/8                                                                  ______________________________________                                         r.sub.1 = 50.993                                                                         d.sub.1 = 12.266                                                                          n.sub.1 = 1.6516                                                                            ν.sub.1 = 58.7                            r.sub.2 = -1149.926                                                                      d.sub.2 = 11.864                                                     r.sub.3 = -47.83                                                                         d.sub.3 = 2.727                                                                           n.sub.2 = 1.5927                                                                            ν.sub.2 = 35.3                            r.sub.4 = 36.349                                                                         d.sub.4 = 9.171                                                      r.sub.5 = 118.648                                                                        d.sub.5 = 13.111                                                                          n.sub.3 = 1.6779                                                                            ν.sub.3 = 55.3                            r.sub.6 = 42.559                                                                         f.sub.1 = 75.238                                                                          f.sub.2 = -34.431                                                   f.sub.3 = 47.776                                                                           ##STR10##                                                ______________________________________                                    

wherein the reference symbols r₁ through r₆ represent the radii of curvature of the respective lens surfaces, the symbols d₁ through d₅ represent the axial thicknesses and the axial air spaces of the respective lenses, the symbols n₁ through n₃ represent the refractive indices of the respective lenses, the symbols ν₁ through ν₃ represent the Abbe numbers of the respective lenses and the symbol F represents the aperture ratio, respectively. 